// // boost heap: d-ary heap as container adaptor
//
// Copyright (C) 2010 Tim Blechmann
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_HEAP_D_ARY_HEAP_HPP
#define BOOST_HEAP_D_ARY_HEAP_HPP

#include <algorithm>
#include <utility>
#include <vector>

#include <boost/assert.hpp>

#include <boost/heap/detail/heap_comparison.hpp>
#include <boost/heap/detail/mutable_heap.hpp>
#include <boost/heap/detail/ordered_adaptor_iterator.hpp>
#include <boost/heap/detail/stable_heap.hpp>
#include <boost/mem_fn.hpp>

#ifdef BOOST_HAS_PRAGMA_ONCE
#    pragma once
#endif


#ifndef BOOST_DOXYGEN_INVOKED
#    ifdef BOOST_HEAP_SANITYCHECKS
#        define BOOST_HEAP_ASSERT BOOST_ASSERT
#    else
#        define BOOST_HEAP_ASSERT( expression )
#    endif
#endif

namespace boost { namespace heap {
namespace detail {

struct nop_index_updater
{
    template < typename T >
    static void run( T&, std::size_t )
    {}
};

typedef parameter::parameters< boost::parameter::required< tag::arity >,
                               boost::parameter::optional< tag::allocator >,
                               boost::parameter::optional< tag::compare >,
                               boost::parameter::optional< tag::stable >,
                               boost::parameter::optional< tag::stability_counter_type >,
                               boost::parameter::optional< tag::constant_time_size > >
    d_ary_heap_signature;


/* base class for d-ary heap */
template < typename T, class BoundArgs, class IndexUpdater >
class d_ary_heap : private make_heap_base< T, BoundArgs, false >::type
{
    typedef make_heap_base< T, BoundArgs, false > heap_base_maker;

    typedef typename heap_base_maker::type  super_t;
    typedef typename super_t::internal_type internal_type;

    typedef typename boost::allocator_rebind< typename heap_base_maker::allocator_argument, internal_type >::type
                                                                  internal_type_allocator;
    typedef std::vector< internal_type, internal_type_allocator > container_type;
    typedef typename container_type::const_iterator               container_iterator;

    typedef IndexUpdater index_updater;

    container_type q_;

    static const unsigned int D = parameter::binding< BoundArgs, tag::arity >::type::value;

    template < typename Heap1, typename Heap2 >
    friend struct heap_merge_emulate;

    struct implementation_defined : extract_allocator_types< typename heap_base_maker::allocator_argument >
    {
        typedef T value_type;
        typedef
            typename detail::extract_allocator_types< typename heap_base_maker::allocator_argument >::size_type size_type;

        typedef typename heap_base_maker::compare_argument   value_compare;
        typedef typename heap_base_maker::allocator_argument allocator_type;

        struct ordered_iterator_dispatcher
        {
            static size_type max_index( const d_ary_heap* heap )
            {
                return heap->q_.size() - 1;
            }

            static bool is_leaf( const d_ary_heap* heap, size_type index )
            {
                return !heap->not_leaf( index );
            }

            static std::pair< size_type, size_type > get_child_nodes( const d_ary_heap* heap, size_type index )
            {
                BOOST_HEAP_ASSERT( !is_leaf( heap, index ) );
                return std::make_pair( d_ary_heap::first_child_index( index ), heap->last_child_index( index ) );
            }

            static internal_type const& get_internal_value( const d_ary_heap* heap, size_type index )
            {
                return heap->q_[ index ];
            }

            static value_type const& get_value( internal_type const& arg )
            {
                return super_t::get_value( arg );
            }
        };

        typedef detail::ordered_adaptor_iterator< const value_type,
                                                  internal_type,
                                                  d_ary_heap,
                                                  allocator_type,
                                                  typename super_t::internal_compare,
                                                  ordered_iterator_dispatcher >
            ordered_iterator;

        typedef detail::stable_heap_iterator< const value_type, container_iterator, super_t > iterator;
        typedef iterator                                                                      const_iterator;
        typedef void*                                                                         handle_type;
    };

    typedef typename implementation_defined::ordered_iterator_dispatcher ordered_iterator_dispatcher;

public:
    typedef T value_type;

    typedef typename implementation_defined::size_type        size_type;
    typedef typename implementation_defined::difference_type  difference_type;
    typedef typename implementation_defined::value_compare    value_compare;
    typedef typename implementation_defined::allocator_type   allocator_type;
    typedef typename implementation_defined::reference        reference;
    typedef typename implementation_defined::const_reference  const_reference;
    typedef typename implementation_defined::pointer          pointer;
    typedef typename implementation_defined::const_pointer    const_pointer;
    typedef typename implementation_defined::iterator         iterator;
    typedef typename implementation_defined::const_iterator   const_iterator;
    typedef typename implementation_defined::ordered_iterator ordered_iterator;
    typedef typename implementation_defined::handle_type      handle_type;

    static const bool is_stable = extract_stable< BoundArgs >::value;

    explicit d_ary_heap( value_compare const& cmp = value_compare() ) :
        super_t( cmp )
    {}

    d_ary_heap( d_ary_heap const& rhs ) :
        super_t( rhs ),
        q_( rhs.q_ )
    {}

#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
    d_ary_heap( d_ary_heap&& rhs ) :
        super_t( std::move( rhs ) ),
        q_( std::move( rhs.q_ ) )
    {}

    d_ary_heap& operator=( d_ary_heap&& rhs )
    {
        super_t::operator=( std::move( rhs ) );
        q_ = std::move( rhs.q_ );
        return *this;
    }
#endif

    d_ary_heap& operator=( d_ary_heap const& rhs )
    {
        static_cast< super_t& >( *this ) = static_cast< super_t const& >( rhs );
        q_                               = rhs.q_;
        return *this;
    }

    bool empty( void ) const
    {
        return q_.empty();
    }

    size_type size( void ) const
    {
        return q_.size();
    }

    size_type max_size( void ) const
    {
        return q_.max_size();
    }

    void clear( void )
    {
        q_.clear();
    }

    allocator_type get_allocator( void ) const
    {
        return q_.get_allocator();
    }

    value_type const& top( void ) const
    {
        BOOST_ASSERT( !empty() );
        return super_t::get_value( q_.front() );
    }

    void push( value_type const& v )
    {
        q_.push_back( super_t::make_node( v ) );
        reset_index( size() - 1, size() - 1 );
        siftup( q_.size() - 1 );
    }

#if !defined( BOOST_NO_CXX11_RVALUE_REFERENCES ) && !defined( BOOST_NO_CXX11_VARIADIC_TEMPLATES )
    template < class... Args >
    void emplace( Args&&... args )
    {
        q_.emplace_back( super_t::make_node( std::forward< Args >( args )... ) );
        reset_index( size() - 1, size() - 1 );
        siftup( q_.size() - 1 );
    }
#endif
    void pop( void )
    {
        BOOST_ASSERT( !empty() );
        std::swap( q_.front(), q_.back() );
        q_.pop_back();

        if ( q_.empty() )
            return;

        reset_index( 0, 0 );
        siftdown( 0 );
    }

    void swap( d_ary_heap& rhs )
    {
        super_t::swap( rhs );
        q_.swap( rhs.q_ );
    }

    iterator begin( void ) const
    {
        return iterator( q_.begin() );
    }

    iterator end( void ) const
    {
        return iterator( q_.end() );
    }

    ordered_iterator ordered_begin( void ) const
    {
        return ordered_iterator( 0, this, super_t::get_internal_cmp() );
    }

    ordered_iterator ordered_end( void ) const
    {
        return ordered_iterator( size(), this, super_t::get_internal_cmp() );
    }

    void reserve( size_type element_count )
    {
        q_.reserve( element_count );
    }

    value_compare const& value_comp( void ) const
    {
        return super_t::value_comp();
    }

private:
    void reset_index( size_type index, size_type new_index )
    {
        BOOST_HEAP_ASSERT( index < q_.size() );
        index_updater::run( q_[ index ], new_index );
    }

    void siftdown( size_type index )
    {
        while ( not_leaf( index ) ) {
            size_type max_child_index = top_child_index( index );
            if ( !super_t::operator()( q_[ max_child_index ], q_[ index ] ) ) {
                reset_index( index, max_child_index );
                reset_index( max_child_index, index );
                std::swap( q_[ max_child_index ], q_[ index ] );
                index = max_child_index;
            } else
                return;
        }
    }

    /* returns new index */
    void siftup( size_type index )
    {
        while ( index != 0 ) {
            size_type parent = parent_index( index );

            if ( super_t::operator()( q_[ parent ], q_[ index ] ) ) {
                reset_index( index, parent );
                reset_index( parent, index );
                std::swap( q_[ parent ], q_[ index ] );
                index = parent;
            } else
                return;
        }
    }

    bool not_leaf( size_type index ) const
    {
        const size_t first_child = first_child_index( index );
        return first_child < q_.size();
    }

    size_type top_child_index( size_type index ) const
    {
        // invariant: index is not a leaf, so the iterator range is not empty

        const size_t                                    first_index = first_child_index( index );
        typedef typename container_type::const_iterator container_iterator;

        const container_iterator first_child = q_.begin() + first_index;
        const container_iterator end         = q_.end();

        const size_type max_elements = std::distance( first_child, end );

        const container_iterator last_child = ( max_elements > D ) ? first_child + D : end;

        const container_iterator min_element
            = std::max_element( first_child, last_child, static_cast< super_t const& >( *this ) );

        return min_element - q_.begin();
    }

    static size_type parent_index( size_type index )
    {
        return ( index - 1 ) / D;
    }

    static size_type first_child_index( size_type index )
    {
        return index * D + 1;
    }

    size_type last_child_index( size_type index ) const
    {
        const size_t    first_index = first_child_index( index );
        const size_type last_index  = ( std::min )( first_index + D - 1, size() - 1 );

        return last_index;
    }

    template < typename U, typename V, typename W, typename X >
    struct rebind
    {
        typedef d_ary_heap< U,
                            typename d_ary_heap_signature::bind<
                                boost::heap::stable< heap_base_maker::is_stable >,
                                boost::heap::stability_counter_type< typename heap_base_maker::stability_counter_type >,
                                boost::heap::arity< D >,
                                boost::heap::compare< V >,
                                boost::heap::allocator< W > >::type,
                            X >
            other;
    };

    template < class U >
    friend class priority_queue_mutable_wrapper;

    void update( size_type index )
    {
        if ( index == 0 ) {
            siftdown( index );
            return;
        }
        size_type parent = parent_index( index );

        if ( super_t::operator()( q_[ parent ], q_[ index ] ) )
            siftup( index );
        else
            siftdown( index );
    }

    void erase( size_type index )
    {
        while ( index != 0 ) {
            size_type parent = parent_index( index );

            reset_index( index, parent );
            reset_index( parent, index );
            std::swap( q_[ parent ], q_[ index ] );
            index = parent;
        }
        pop();
    }

    void increase( size_type index )
    {
        siftup( index );
    }

    void decrease( size_type index )
    {
        siftdown( index );
    }
};


template < typename T, typename BoundArgs >
struct select_dary_heap
{
    static const bool is_mutable = extract_mutable< BoundArgs >::value;

    typedef typename boost::conditional< is_mutable,
                                         priority_queue_mutable_wrapper< d_ary_heap< T, BoundArgs, nop_index_updater > >,
                                         d_ary_heap< T, BoundArgs, nop_index_updater > >::type type;
};

} /* namespace detail */


/**
 * \class d_ary_heap
 * \brief d-ary heap class
 *
 * This class implements an immutable priority queue. Internally, the d-ary heap is represented
 * as dynamically sized array (std::vector), that directly stores the values.
 *
 * The template parameter T is the type to be managed by the container.
 * The user can specify additional options and if no options are provided default options are used.
 *
 * The container supports the following options:
 * - \c boost::heap::arity<>, required
 * - \c boost::heap::compare<>, defaults to \c compare<std::less<T> >
 * - \c boost::heap::stable<>, defaults to \c stable<false>
 * - \c boost::heap::stability_counter_type<>, defaults to \c stability_counter_type<boost::uintmax_t>
 * - \c boost::heap::allocator<>, defaults to \c allocator<std::allocator<T> >
 * - \c boost::heap::mutable_<>, defaults to \c mutable_<false>
 *
 */
#ifdef BOOST_DOXYGEN_INVOKED
template < class T, class... Options >
#else
template < typename T,
           class A0 = boost::parameter::void_,
           class A1 = boost::parameter::void_,
           class A2 = boost::parameter::void_,
           class A3 = boost::parameter::void_,
           class A4 = boost::parameter::void_,
           class A5 = boost::parameter::void_ >
#endif
class d_ary_heap :
    public detail::select_dary_heap< T, typename detail::d_ary_heap_signature::bind< A0, A1, A2, A3, A4, A5 >::type >::type
{
    typedef typename detail::d_ary_heap_signature::bind< A0, A1, A2, A3, A4, A5 >::type bound_args;
    typedef typename detail::select_dary_heap< T, bound_args >::type                    super_t;

    template < typename Heap1, typename Heap2 >
    friend struct heap_merge_emulate;

#ifndef BOOST_DOXYGEN_INVOKED
    static const bool is_mutable = detail::extract_mutable< bound_args >::value;

#    define BOOST_HEAP_TYPEDEF_FROM_SUPER_T( NAME ) typedef typename super_t::NAME NAME;

    struct implementation_defined
    {
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( size_type )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( difference_type )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( value_compare )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( allocator_type )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( reference )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( const_reference )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( pointer )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( const_pointer )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( iterator )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( const_iterator )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( ordered_iterator )
        BOOST_HEAP_TYPEDEF_FROM_SUPER_T( handle_type )
    };
#    undef BOOST_HEAP_TYPEDEF_FROM_SUPER_T

#endif
public:
    static const bool constant_time_size    = true;
    static const bool has_ordered_iterators = true;
    static const bool is_mergable           = false;
    static const bool has_reserve           = true;
    static const bool is_stable             = super_t::is_stable;

    typedef T                                                 value_type;
    typedef typename implementation_defined::size_type        size_type;
    typedef typename implementation_defined::difference_type  difference_type;
    typedef typename implementation_defined::value_compare    value_compare;
    typedef typename implementation_defined::allocator_type   allocator_type;
    typedef typename implementation_defined::reference        reference;
    typedef typename implementation_defined::const_reference  const_reference;
    typedef typename implementation_defined::pointer          pointer;
    typedef typename implementation_defined::const_pointer    const_pointer;
    /// \copydoc boost::heap::priority_queue::iterator
    typedef typename implementation_defined::iterator         iterator;
    typedef typename implementation_defined::const_iterator   const_iterator;
    typedef typename implementation_defined::ordered_iterator ordered_iterator;
    typedef typename implementation_defined::handle_type      handle_type;

    /// \copydoc boost::heap::priority_queue::priority_queue(value_compare const &)
    explicit d_ary_heap( value_compare const& cmp = value_compare() ) :
        super_t( cmp )
    {}

    /// \copydoc boost::heap::priority_queue::priority_queue(priority_queue const &)
    d_ary_heap( d_ary_heap const& rhs ) :
        super_t( rhs )
    {}

#ifndef BOOST_NO_CXX11_RVALUE_REFERENCES
    /// \copydoc boost::heap::priority_queue::priority_queue(priority_queue &&)
    d_ary_heap( d_ary_heap&& rhs ) :
        super_t( std::move( rhs ) )
    {}

    /// \copydoc boost::heap::priority_queue::operator=(priority_queue &&)
    d_ary_heap& operator=( d_ary_heap&& rhs )
    {
        super_t::operator=( std::move( rhs ) );
        return *this;
    }
#endif

    /// \copydoc boost::heap::priority_queue::operator=(priority_queue const &)
    d_ary_heap& operator=( d_ary_heap const& rhs )
    {
        super_t::operator=( rhs );
        return *this;
    }

    /// \copydoc boost::heap::priority_queue::empty
    bool empty( void ) const
    {
        return super_t::empty();
    }

    /// \copydoc boost::heap::priority_queue::size
    size_type size( void ) const
    {
        return super_t::size();
    }

    /// \copydoc boost::heap::priority_queue::max_size
    size_type max_size( void ) const
    {
        return super_t::max_size();
    }

    /// \copydoc boost::heap::priority_queue::clear
    void clear( void )
    {
        super_t::clear();
    }

    /// \copydoc boost::heap::priority_queue::get_allocator
    allocator_type get_allocator( void ) const
    {
        return super_t::get_allocator();
    }

    /// \copydoc boost::heap::priority_queue::top
    value_type const& top( void ) const
    {
        return super_t::top();
    }

    /// \copydoc boost::heap::priority_queue::push
    typename boost::conditional< is_mutable, handle_type, void >::type push( value_type const& v )
    {
        return super_t::push( v );
    }

#if !defined( BOOST_NO_CXX11_RVALUE_REFERENCES ) && !defined( BOOST_NO_CXX11_VARIADIC_TEMPLATES )
    /// \copydoc boost::heap::priority_queue::emplace
    template < class... Args >
    typename boost::conditional< is_mutable, handle_type, void >::type emplace( Args&&... args )
    {
        return super_t::emplace( std::forward< Args >( args )... );
    }
#endif

    /// \copydoc boost::heap::priority_queue::operator<(HeapType const & rhs) const
    template < typename HeapType >
    bool operator<( HeapType const& rhs ) const
    {
        return detail::heap_compare( *this, rhs );
    }

    /// \copydoc boost::heap::priority_queue::operator>(HeapType const & rhs) const
    template < typename HeapType >
    bool operator>( HeapType const& rhs ) const
    {
        return detail::heap_compare( rhs, *this );
    }

    /// \copydoc boost::heap::priority_queue::operator>=(HeapType const & rhs) const
    template < typename HeapType >
    bool operator>=( HeapType const& rhs ) const
    {
        return !operator<( rhs );
    }

    /// \copydoc boost::heap::priority_queue::operator<=(HeapType const & rhs) const
    template < typename HeapType >
    bool operator<=( HeapType const& rhs ) const
    {
        return !operator>( rhs );
    }

    /// \copydoc boost::heap::priority_queue::operator==(HeapType const & rhs) const
    template < typename HeapType >
    bool operator==( HeapType const& rhs ) const
    {
        return detail::heap_equality( *this, rhs );
    }

    /// \copydoc boost::heap::priority_queue::operator!=(HeapType const & rhs) const
    template < typename HeapType >
    bool operator!=( HeapType const& rhs ) const
    {
        return !( *this == rhs );
    }

    /**
     * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Requirement: data structure must be configured as mutable
     * */
    void update( handle_type handle, const_reference v )
    {
        BOOST_STATIC_ASSERT( is_mutable );
        super_t::update( handle, v );
    }

    /**
     * \b Effects: Updates the heap after the element handled by \c handle has been changed.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: If this is not called, after a handle has been updated, the behavior of the data structure is undefined!
     *
     * \b Requirement: data structure must be configured as mutable
     * */
    void update( handle_type handle )
    {
        BOOST_STATIC_ASSERT( is_mutable );
        super_t::update( handle );
    }

    /**
     * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: The new value is expected to be greater than the current one
     *
     * \b Requirement: data structure must be configured as mutable
     * */
    void increase( handle_type handle, const_reference v )
    {
        BOOST_STATIC_ASSERT( is_mutable );
        super_t::increase( handle, v );
    }

    /**
     * \b Effects: Updates the heap after the element handled by \c handle has been changed.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: The new value is expected to be greater than the current one. If this is not called, after a handle has
     * been updated, the behavior of the data structure is undefined!
     *
     * \b Requirement: data structure must be configured as mutable
     * */
    void increase( handle_type handle )
    {
        BOOST_STATIC_ASSERT( is_mutable );
        super_t::increase( handle );
    }

    /**
     * \b Effects: Assigns \c v to the element handled by \c handle & updates the priority queue.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: The new value is expected to be less than the current one
     *
     * \b Requirement: data structure must be configured as mutable
     * */
    void decrease( handle_type handle, const_reference v )
    {
        BOOST_STATIC_ASSERT( is_mutable );
        super_t::decrease( handle, v );
    }

    /**
     * \b Effects: Updates the heap after the element handled by \c handle has been changed.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Note: The new value is expected to be less than the current one. If this is not called, after a handle has
     * been updated, the behavior of the data structure is undefined!
     *
     * \b Requirement: data structure must be configured as mutable
     * */
    void decrease( handle_type handle )
    {
        BOOST_STATIC_ASSERT( is_mutable );
        super_t::decrease( handle );
    }

    /**
     * \b Effects: Removes the element handled by \c handle from the priority_queue.
     *
     * \b Complexity: Logarithmic.
     *
     * \b Requirement: data structure must be configured as mutable
     * */
    void erase( handle_type handle )
    {
        BOOST_STATIC_ASSERT( is_mutable );
        super_t::erase( handle );
    }

    /**
     * \b Effects: Casts an iterator to a node handle.
     *
     * \b Complexity: Constant.
     *
     * \b Requirement: data structure must be configured as mutable
     * */
    static handle_type s_handle_from_iterator( iterator const& it )
    {
        BOOST_STATIC_ASSERT( is_mutable );
        return super_t::s_handle_from_iterator( it );
    }

    /// \copydoc boost::heap::priority_queue::pop
    void pop( void )
    {
        super_t::pop();
    }

    /// \copydoc boost::heap::priority_queue::swap
    void swap( d_ary_heap& rhs )
    {
        super_t::swap( rhs );
    }

    /// \copydoc boost::heap::priority_queue::begin
    const_iterator begin( void ) const
    {
        return super_t::begin();
    }

    /// \copydoc boost::heap::priority_queue::begin
    iterator begin( void )
    {
        return super_t::begin();
    }

    /// \copydoc boost::heap::priority_queue::end
    iterator end( void )
    {
        return super_t::end();
    }

    /// \copydoc boost::heap::priority_queue::end
    const_iterator end( void ) const
    {
        return super_t::end();
    }

    /// \copydoc boost::heap::fibonacci_heap::ordered_begin
    ordered_iterator ordered_begin( void ) const
    {
        return super_t::ordered_begin();
    }

    /// \copydoc boost::heap::fibonacci_heap::ordered_end
    ordered_iterator ordered_end( void ) const
    {
        return super_t::ordered_end();
    }

    /// \copydoc boost::heap::priority_queue::reserve
    void reserve( size_type element_count )
    {
        super_t::reserve( element_count );
    }

    /// \copydoc boost::heap::priority_queue::value_comp
    value_compare const& value_comp( void ) const
    {
        return super_t::value_comp();
    }
};

}} // namespace boost::heap

#undef BOOST_HEAP_ASSERT

#endif /* BOOST_HEAP_D_ARY_HEAP_HPP */
